Djairo G. de Figueiredo - Selected Papers

733 Pages·2013·32.392 MB·English

by  Djairo G. de Figueiredo (auth.), David G. Costa (eds.)

djairo g. de figueiredo
Selected Papers
123
DJAIRO G. de FIGUEIREDO –
Selected Papers
Djairo G. de Figueiredo
Photo by Christina Figueiredo Prudencio
DJAIRO G. de FIGUEIREDO –
Selected Papers
Edited by
David G. Costa
DJAIRO G. de
FIGUEIREDO –
Selected Papers
123
Djairo G.de Figueiredo
IMECC-UNICAMP
Cidade Universitaria InstitutodeMatematica
Estatistica eComputac¸a˜oCientifica
Campinas
Sa˜oPaulo
Brazil
Editor
DavidG. Costa
Department ofMathematical Sciences
Universityof NevadaLas Vegas
LasVegas, NV
USA
ISBN 978-3-319-02855-2 ISBN978-3-319-02856-9 (eBook)
DOI 10.1007/978-3-319-02856-9
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012954381
Math. Subj.Classification(2010): 35J2035J50,35J60,35J65,45G99, 46E35,58E99
(cid:2)SpringerInternationalPublishingSwitzerland2013
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Selected Works of Outstanding
Brazilian Mathematicians
Mathematics in Brazil is a very young endeavor. Regular research activities
and graduate studies go back to the 1950s, when the biannual Brazilian
Mathematical Colloquium was launched and Brazil joined the International
Mathematical Union (IMU). The Instituto de Matema´tica Pura e Aplicada
(IMPA) was founded in 1952. Creation of the SBM, Sociedade Brasileira de
Matema´tica, would follow, in 1969.
Halfacenturylater,BrazilhasreachedGroupIVintheIMU’srankingand
is responsible for about 1.8 % of the world’s mathematical production
(according to MathSciNet). The Brazilian mathematical community is
growing steadily, and has earned international reputation in several fields of
research. While many great challenges remain ahead, one can certainly be
proud of what has been achieved in such a short time.
Thisprogresswaslargelyduetoanumberofleadingmathematicianswho,
in addition to their own fundamental contributions to Mathematics, created
genuine ‘‘schools’’ around them that raised entire research fields in Brazil to
thebestinternationalstandards.Throughthiscollection,theSBMandIMPA
aim to highlight their scientific trajectories and to pay tribute to their
pioneering efforts.
Editors
Hila´rio Alencar
Ce´sar Camacho
Andre´ Nachbin
Marcelo Viana
v
Preface
DjairoGuedesdeFigueiredohashadamajorinfluenceinthedevelopmentof
the area of Analysis, particularly in its applications to problems in Partial
Differential Equations (PDEs) for equations and systems of elliptic type by
meansofvariationalandtopologicaltechniques.Asamathematicianlivingin
his native country of Brazil, his guidance of students, his publication of 29
books and monographs, and collaboration with many colleagues (myself
included) has been instrumental in creating a whole generation of researchers
andvarious seminalgroupsinPDEsthroughoutthecountry.Inaddition,his
respectedstatusintheinternationalmathematicalcommunityhascontributed
to the establishment of several collaborative programs of Brazil with other
countries, especially Belgium and Italy.
The present volume contains a selection of papers of Djairo (as he is
commonly addressed) spanning the areas of geometry of Banach spaces,
monotone operators, and boundary value problems for scalar equations and
systemsofellipticPDEs.Inaddition,acompletelistofhisresearchoutputof
over 100 papers, including 40 collaborators, and the names and professional
affiliations of his 26 (and counting) Ph.D. students is provided. Finally, a
biographical account of Djairo’s professional life (by Djairo, himself) is
included in this volume of his selected works.
More often than not, especially through meetings in honor of Djairo, his
students and colleagues have expressed their admiration and thanks for his
guidance, inspiration and friendship.
I feel honored and privileged to have known, collaborated with, and
enjoyed Djairo’s friendship for the past nearly four decades.
Las Vegas David G. Costa
vii
Acknowledgments
TheBrazilianMathematicalSociety(SBM),theInstituteforPureandApplied
Mathematics (IMPA) and Springer-Verlag express their gratitude to the fol-
lowing copyright holders for granting permisson to reprint the publications
below. Also find below a list of publications from Springer-Verlag whose
reprints will be included in this volume.
American Mathematical Society
De Figueiredo, D.G.; Karlovitz, L.A., On the Radial Projection in Normed
Spaces, Bull. Amer. Math. Soc. 73 (1967), 364–368.
Browder, F.E.; De Figueiredo, D.G.; Gupta, C.P., Maximal Monotone
Operators and Nonlinear Integral Equations of Hammerstein Type, Bull.
Amer. Math. Soc. 76 (1970), 700–705.
De Figueiredo, D.G.; Gupta, C.P., On the Variational Method for the
ExistenceofSolutionsofNonlinearEquationsofHammersteinType,Proc.
Amer. Math. Soc. 40 (1973), 470–476.
De Figueiredo, D.G., Positive Solutions for Some Classes of Semilinear
Elliptic Problems, Nonlinear Functional Analysis and its Applications,
Proc. Sympos. Pure Math. 45, Part 1, Amer. Math. Soc. (1986), 371–379.
De Figueiredo, D.G.; Felmer, P., On Superquadratic Elliptic Systems, Trans.
Amer. Math. Soc. 343 (1994), 99–116.
De Figueiredo, D.G.; Ding, Y.H, Strongly Indefinite Functionals and
Multiple Solutions of Elliptic Systems, Trans. Amer. Math. Soc. 355
(2003), 2973–2989.
ix
Acknowledgments
Annali della Scuola Normale Superiore
De Figueiredo, D.G.; Felmer, P., A Liouville-Type Theorem for Elliptic
Systems, Ann. Scuola Norm. Sup. Pisa XXI (1994), 387–397.
American Institute of Mathematical Sciences
De Figueiredo, D.G.; Ding, Y., Solutions of a Nonlinear Schrodinger
Equation, Discrete Cont. Dyn. Syst. 8 (2002), 563–584.
De Gruyter
DeFigueiredo,D.G.;Ruf,B.,OnaSuperlinearSturm-LiouvilleEquationand
a Related Bouncing Problem, J. Reine Angew. Math. 421 (1991), 1–22.
Elsevier
DeFigueiredo,D.G.;Karlovitz,L.A.,TheExtensionofContractionsandthe
IntersectionofBallsinBanachSpaces,J.Funct.Anal.11(1972),168–178.
De Figueiredo, D.G.; Gossez, J.-P., Nonlinear Perturbations of a Linear
Elliptic Problem near its First Eigenvalue, J. Differential Equations 30
(1978), 1–19.
De Figueiredo, D.G.; Ni, W.-M.; Perturbations of Second Order Linear
Elliptic Problems by Nolinearities without Landesman-Lazer Condition,
Nonlinear Anal. 3 (1979), 629–634.
DeFigueiredo,D,G,,SemilinearEquationsatResonance:HigherEigenvalues
and Unbounded Nonlinearities, Recent Advances in Differential Equa-
tions, Ed. Roberto Conti, Academic Press (1981), 89–99.
De Figueiredo, D.G.; Lions P.-L.; Nussbaum, R.D., A Priori Estimates and
Existence of Positive Solutions of Semilinear Elliptic Equations, J. Math.
Pures Appl. 61 (1982), 41–63.
De Figueiredo, D.G., On the Superlinear Ambrosetti-Prodi Problem,
Nonlineal Anal. 8 (1984), 655–665.
Costa,D.G.;DeFigueiredo,D.G.,RadialSolutionsofaDirichletProblemin
a Ball, J. Differential Equations 60 (1985), 80–89.
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Acknowledgments
Costa, D.G.; De Figueiredo, D.G.; Gonc¸alves, J.V.A., On the Uniqueness of
SolutionforaClassofSuperlinearEllipticProblems,J.Math.Anal.Appl.
123 (1987), 170–180.
Costa, D.G.; De Figueiredo, D.G.; Srikanth, P.N., The Exact Number of
Solutions for a Class of Ordinary Differential Equations through Morse
Index Computation, J. Differential Equations 96 (1992), 185–199.
De Figueiredo, D.G.;Yang, J., Decay, Symmetry and Existence of Solutions
of Semilinear Elliptic Systems, Nonlinear Anal. 33 (1998), 211–234.
De Figueiredo, D.G.; Gossez, J.-P.; Ubilla, P., Local Superlinearity and
SublinearityforIndefiniteSemilinearEllipticProblems,J.Funct.Anal.199
(2003), 452–467.
De Figueiredo, D.G.; Do O´ , J.M.; Ruf, B., An Orlicz-Space Approach to
Superlinear Elliptic Systems, J. Funct. Anal. 224 (2005), 471–496.
DeFigueiredo,D.G.;Sirakov,B.,OntheAmbrosetti-ProdiProblemforNon-
VariationalEllipticSystems,J.DifferentialEquations240(2007),357–374.
De Figueiredo, D.G.; Lopes, O., Solitary Waves for some Nonlinear
Schrodinger Systems, Ann. Inst. H. Poincare, Anal. Non Lineaire 25
(2008), 149–161.
De Figueiredo, D.G.; Gossez, J.-P.; Ubilla, P., Local ‘Superlinearity’ and
‘Sublinearity’ for the p-Laplacian, J. Funct. Anal. 257 (2009), 721–752.
Indiana University
De Figueiredo, D.G.; Lions, P.-L., On Pairs of Positive Solutions for a Class
ofSemilinearEllipticProblems,IndianaUniv.Math.J.34(1985),591–606.
Rendiconti dell’Istituto di Matematica dell’Universita` di Trieste
De Figueiredo, D.G.; Mitidieri, E., Maximum Principles for Linear Elliptic
Systems, Univ. Trieste, Vol. XXII (1990), 36–66.
Rocky Mountain Mathematics Consortium
De Figueiredo, D.G., On Superlinear Elliptic Problems with Nonlinearities
Interacting only with Higher Eigenvalues, Rocky Mountain J. Math. 18
(1988), 287–303.
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